How to characterize the landscape of overparameterized convolutional neural networks

Yihong Gu, Weizhong Zhang, Cong Fang, Jason D. Lee, Tong Zhang

Research output: Contribution to journalConference articlepeer-review

7 Scopus citations


For many initialization schemes, parameters of two randomly initialized deep neural networks (DNNs) can be quite different, but feature distributions of the hidden nodes are similar at each layer. With the help of a new technique called neural network grafting, we demonstrate that even during the entire training process, feature distributions of differently initialized networks remain similar at each layer. In this paper, we present an explanation of this phenomenon. Specifically, we consider the loss landscape of an overparameterized convolutional neural network (CNN) in the continuous limit, where the numbers of channels/hidden nodes in the hidden layers go to infinity. Although the landscape of the overparameterized CNN is still non-convex with respect to the trainable parameters, we show that very surprisingly, it can be reformulated as a convex function with respect to the feature distributions in the hidden layers. Therefore by reparameterizing neural networks in terms of feature distributions, we obtain a much simpler characterization of the landscape of overparameterized CNNs. We further argue that training with respect to network parameters leads to a fixed trajectory in the feature distributions.

Original languageEnglish (US)
JournalAdvances in Neural Information Processing Systems
StatePublished - 2020
Event34th Conference on Neural Information Processing Systems, NeurIPS 2020 - Virtual, Online
Duration: Dec 6 2020Dec 12 2020

All Science Journal Classification (ASJC) codes

  • Computer Networks and Communications
  • Information Systems
  • Signal Processing


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